CN105041293A - System and method for monitoring drilling systems - Google Patents

System and method for monitoring drilling systems Download PDF

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CN105041293A
CN105041293A CN201510209777.3A CN201510209777A CN105041293A CN 105041293 A CN105041293 A CN 105041293A CN 201510209777 A CN201510209777 A CN 201510209777A CN 105041293 A CN105041293 A CN 105041293A
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詹晟
赵金海
郑和荣
许卫平
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China Petroleum and Chemical Corp
Sinopec Tech Houston LLC
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Sinopec Tech Houston LLC
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    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21BEARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B44/00Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21BEARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B12/00Accessories for drilling tools
    • E21B12/02Wear indicators
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/18Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04Ageing analysis or optimisation against ageing

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Abstract

The present disclosure provides methods and systems for monitoring a drilling system, including methods and systems for estimating the life consumption of downhole drilling tools. The system employs a plurality of sensors that provide sensor signals related to the status of components in the drilling system. The sensor signals are analyzed using Functional Principal Component Analysis (FPCA) to give estimations for one or more performance metrics, including the life consumption of downhole drilling tools.

Description

System and method for monitoring a drilling system
Technical Field
The present invention relates to systems and methods for monitoring drilling systems for oil and gas exploration, and more particularly to systems and methods for estimating life consumption and life of downhole drilling tools in real time.
Background
Drilling systems are used in the sophisticated electromechanical systems of modern oil and gas exploration. The drilling system includes an above-ground component and a downhole drilling tool. The drilling assembly is a downhole drilling tool that breaks through and penetrates subterranean formations. The drilling assembly includes a drill bit and a drill collar. It may also include downhole motors, rotary steerable systems, telemetry transmitters, as well as Measurement While Drilling (MWD) instruments and Logging While Drilling (LWD) instruments. Although MWD refers to the measurement of the movement and position of the drilling assembly while drilling continues, and LWD focuses more on the measurement of formation properties, the two may be used interchangeably in this disclosure.
Formation properties measured during drilling typically include resistivity, density, porosity, permeability, acoustic properties, nuclear magnetic resonance properties, corrosion characteristics of the fluid or formation, and salt or brine content. The measured drilling assembly parameters typically include velocity, vibration, bending moment, and the like. Downhole vibrations can also be classified as: axial vibration along the drill string axis (e.g., bit bounce); lateral vibration (e.g., whirl) transverse to the drill string axis; and torsional vibrations (e.g., stick-slip) that are in a rotational path about the drill string axis. The MWD/LWD tool also monitors drilling operation parameters including Weight On Bit (WOB), drilling fluid flow rate, pressure, temperature, permeability, azimuth, toolface, bit rotation, etc.
Wireline logging may be used to examine the formation instead of, or in addition to, MWD/LWD tools. Typically, after the drill string is removed from the borehole, the sonde is lowered to the bottom of the region of interest and then pulled up. In the upward travel, the sonde measures formation properties along its path.
Sensors are used to obtain measurements on MWD/LWD instruments and wireline logging methods. Other electronic components include active components such as Printed Circuit Board Assemblies (PCBA) and transistors, or passive components such as resistors and capacitors. The use of PCBA is distributed throughout the drilling assembly. For example, the PCBA may be used in the operation of power supplies, temperature sensors, pressure sensors, batteries, and the like. The main memory circuit board, reader circuit board, transmitter or receiver circuit board, and accelerator circuit board in a PCBA are commonly used in downhole environments.
The PCBA may be attached to the various sensors of the drilling assembly by any known method. In some embodiments, the sensor may be integrated in the PCBA, for example on a main memory circuit board. The sensors may be measurement sensors that monitor real-time conditions during drilling. In other embodiments, the sensor may be a prognostic sensor. Prognostic sensors are subject to more severe conditions (e.g., higher temperatures or pressures) than normal drilling operations, and thus they are inadequate at accelerated rates. The prognostic sensor can be used to estimate the time to failure of another component.
In addition to monitoring the PCBA status, the sensors may be mounted on any other suitable component in the drilling assembly. For example, sensors may be attached to the drill bit to monitor the movement or temperature of the drill bit. Sensors may also be installed along the borehole to monitor the pressure or flow rate of drilling mud along the path, for example. Sensors (e.g., RFID) may even be packed into the fluid of the drilling system and distributed into the formation.
The processor is typically part of the PCBA. The processor is used to receive, store or execute, for example, computer coded data or sensor signals. For example, the processor may be coupled to program modules that provide executable instructions and to recording media that store results of various computations performed by the processor. The sensor signal is an input to the processor.
In addition to the drilling assembly, the drilling system includes a downhole drilling tool, such as drill pipe, casing, and packers that divide the borehole into different sections. The drilling system further comprises: aboveground components or subsystems, drilling mud circulation systems (mud pumps, flow meters, etc.), drilling platforms and hardware associated therewith (valves, manifolds, generators, pumps, etc.), and other monitoring and control systems for the above-ground portion.
Any downtime for repair and maintenance in the drilling system is expensive. Modern oil and gas exploration in deeper downhole and more difficult to reach locations further increases the failure rate and overall cost of the drilling operation. For example, directional drilling systems face a rather harsh operating environment: downhole temperatures exceed 200 ℃, high lateral and axial vibrations at 15g _ RMS (root mean square), and pressures exceed 250000PSI while requiring well distribution up to 15/100 feet. Accordingly, it is more desirable to implement cost-effective maintenance strategies, such as longer run times, less frequent equipment replacement, and less replacement part inventory. To achieve these goals, it is desirable to more closely monitor the condition of the downhole drilling tool and to better understand the environment in which it operates. The present disclosure provides methods and apparatus for monitoring a drilling system, including methods and apparatus for predicting a degradation trend and service life of a downhole drilling tool.
Disclosure of Invention
The present disclosure provides a method for monitoring a drilling system. The method includes the step of collecting a first set of sensor signals. The sensor signals are from sensors distributed throughout a drilling system including a downhole drilling tool having mechanical and electrical components. The sensor signals reflect one or more conditions of a component in the downhole drilling tool, such as temperature, pressure, and vibration. The method further comprises the step of constructing a model using Functional Principal Component Analysis (FPCA) based on the first set of sensor signals. The sensor signals are used to determine model parameters.
Further, after collecting the second set of sensor signals, the model is updated by adjusting model parameters using the second set of sensor signals. The model is used to estimate one or more performance indicators for components in the drilling system, including life consumption and remaining useful life. Thus, the operator may get a real-time estimate of the life consumption of the drilling tool.
The present disclosure also provides a system for monitoring a downhole drilling tool. The system includes a drilling assembly and a plurality of sensors arranged with respect to the drilling assembly, wherein the sensors provide sensor signals associated with the drilling assembly. The system also includes one or more computers having processors, a non-transitory computer-readable medium communicatively coupled to the processors, and a set of processor-executable instructions embodied in the non-transitory computer-readable medium. The instructions are configured to enable a method for monitoring a downhole drilling tool as described herein.
The present disclosure also provides a drilling system. The drilling system includes a downhole drilling tool and a plurality of sensors disposed with respect to the drilling assembly, wherein the plurality of sensors generate sensor signals reflective of a state of one or more components of the downhole drilling tool as the downhole drilling tool traverses a formation. The drilling system also includes a computer configured to implement the method for monitoring a downhole drilling tool described herein.
Drawings
The teachings of the present invention can be readily understood by considering the following detailed description in conjunction with the accompanying drawings.
Fig. 1 illustrates a test data set used in validating the FPCA model of the present disclosure.
Fig. 2 shows an explained variance score (FVE) in response to the number of selected principal components.
Fig. 3 shows a comparison of life consumption estimation and actual life consumption.
Fig. 4 illustrates a method of the present disclosure.
Detailed Description
Reference will now be made in detail to embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. It should be noted that, where appropriate, like or identical reference numerals are used in the figures and indicate like or identical elements.
The drawings depict embodiments of the disclosure for purposes of illustration only. Alternative embodiments will become readily apparent to those skilled in the art from the following description without departing from the general principles of the disclosure.
According to one aspect of the present disclosure, the sensors are distributed throughout a drilling system that includes a downhole drilling tool, and further includes a drilling assembly, a drill pipe, a casing, and a packer. The sensors may be attached to the surface of the component or placed inside the body of the component, such as a drill bit, drill string, downhole motor, drill pipe, drill collar, downhole battery, and downhole generator. Sensors are also used in electronic components such as MWD/LWD instruments.
According to another aspect of the present disclosure, the sensors measure one or more performance indicators of the downhole drilling tool (e.g., vibration, pressure, temperature, Weight On Bit (WOB), RPM) and transmit the sensor signals to a computer system for storage and analysis. The measurement sensor signals report the status of the downhole component. The prognostic sensor signal may not directly reflect the status of the downhole component (e.g., temperature, vibration), but may be associated with the status of that component that is not directly associated with the sensor. For example, a prognostic sensor can be used to predict the life of a PCBA board. To this end, the correlation may first be employed in a controlled environment (e.g., a laboratory) that subjects the sensor to temperatures that are higher (e.g., 20℃ higher) than the PCBA is subjected to. Prognostic sensors will fail more rapidly than PCBA, from which an acceleration factor can be obtained. Utilizing this life-time correlation allows the state of the prognostic sensor to be used in a downhole environment to estimate the state of another component (e.g., PCBA).
According to yet another aspect of the present disclosure, the sensor is mounted on an above-ground component of the drilling system. For example, in a pressure controlled drilling system, a Rotating Control Device (RCD) is a subsystem that employs high pressure seals, bearings, manifolds, and pumps. Sensors are deployed on the RCD to monitor vibration or noise levels of the bearings and high pressure seals. The flowmeter, the pressure sensor, the vibration detector and the temperature sensor are all arranged on the slurry circulating pump.
According to another aspect of the present disclosure, the sensor signals are used to predict or estimate a performance indicator of the downhole drilling tool, the above ground component, or the subsystem. The indicators may include probability of failure, life consumption, and remaining useful life. The sensor signals may be used to perform cumulative damage analysis, decay analysis, and lifecycle management. The information obtained from the sensors can be used to optimize drilling and exploration performance to avoid dead time (NPT) at the drilling site and reduce maintenance and upkeep costs.
According to yet another aspect of the present disclosure, Functional Data Analysis (FDA) is used to estimate performance indicators, such as life consumption, of a drilling tool. A Functional Principal Component Analysis (FPCA) model is constructed for the sensor signals and provides a collection of computational tools to handle decay trends collected from the same type of component for different faults. The capture pattern of the unit-specific FPC scores generated will change in the sensor signals on the individual units, and these scores can be adjusted as new sensor signals are collected. In this case, the sensor signal is also referred to as a degraded signal, since the sensor signal associated with a drilling tool that fails with respect to time reflects the degradation trend of the drilling tool.
The first step in performing FDA analysis is to model FPCA. In this regard, the decaying signal may be described as a smooth curve contaminated by random errors.First consider a signal. So that Xj(tij) As at tijThe ith measurement of the signal at time j, where tijWith time interval T as endpoint:
Xj(tij)=Rj(tij)+ij,i=1,2,…,nj,0≤tij≤T(1)
wherein R isj(tij) Is an uncontaminated signal, andijis to follow a normal distribution N (0, sigma)2) Independent Identically Distributed (IID) random error. According to the Karhunen-loeve theorem, the stochastic process can be represented by an infinite linear combination of orthogonal functions:
<math> <mrow> <msub> <mi>R</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>M</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mo>&infin;</mo> </munderover> <msub> <mi>&theta;</mi> <mi>js</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>&ap;</mo> <msub> <mi>M</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>X</mi> </msub> </munderover> <msub> <mi>&theta;</mi> <mi>js</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein M isX(tij) Is the overall mean curve, ξ, of the signal across all cellss(tij) Is at tijValue of the s-th eigenfunction at time, number N of eigenvalues to be includedXCan be determined based on the interpretation scale of the function change, and θjsIs a unit specific FPCA score. Orthogonal eigen function xisThe set of (t) is interpreted as a basis function for the extended form of the signal, which approximates the signal as closely as possible. In particular, these functions need to satisfy:
<math> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msup> <msub> <mi>&xi;</mi> <msub> <mi>s</mi> <mn>1</mn> </msub> </msub> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>dt</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msup> <msub> <mi>&xi;</mi> <msub> <mi>s</mi> <mn>2</mn> </msub> </msub> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>dt</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <msub> <mi>s</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>&xi;</mi> <msub> <mi>s</mi> <mn>2</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>dt</mi> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>
these eigenfunctions can be estimated in a non-parametric way. Rj(t) is one of the independent implementations of the random signal r (t). The relationship between eigenvalues and eigenfunctions may be at the covariance C of R (t)R(u, v) by Fredhollin integral eigenequation:
<math> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msub> <mi>C</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> <mi>dv</mi> <mo>=</mo> <msub> <mi>&lambda;</mi> <mi>s</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo>&le;</mo> <mi>u</mi> <mo>&le;</mo> <mi>T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
thus, C based on the obtained eigenfunction and eigenvalueR(u, v) the orthogonal expression is:
<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>C</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mo>&infin;</mo> </munderover> <msub> <mi>&lambda;</mi> <mi>s</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&ap;</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>X</mi> </msub> </munderover> <msub> <mi>&lambda;</mi> <mi>s</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo>&le;</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>&le;</mo> <mi>T</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
function score of unit j θjsCan be calculated from:
<math> <mrow> <msub> <mi>&theta;</mi> <mi>js</mi> </msub> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <mo>[</mo> <msub> <mi>R</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>M</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>dt</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>
considering other model parameters, equation (1) becomes:
<math> <mrow> <msub> <mi>X</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>&ap;</mo> <msub> <mi>M</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>X</mi> </msub> </munderover> <msub> <mi>&theta;</mi> <mi>js</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&epsiv;</mi> <mi>ij</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>n</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
once the model is constructed, parameters in the model are estimated, including an overall mean function, an FPCA function score, and the like.
Overall mean function MX(tij) Is estimated by
Covering all available training decay signalsMay be captured by a local weighted smooth scatter plot (LOWESS) technique. A significant advantage of LOWESS is that the process can be modeled without relying on physical knowledge of the process. Gaussian kernel functions have been widely used to achieve a compromise between performance and computational cost. The local approximation can be estimated by substituting a coefficient [ a ] estimated by the following equation0,a1]Local linear kernel regression of (a):
<math> <mrow> <mi>min</mi> <mo>{</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>n</mi> <mi>j</mi> </msub> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> </mrow> <msub> <mi>h</mi> <mi>c</mi> </msub> </mfrac> <mo>)</mo> </mrow> <msup> <mrow> <mo>[</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>
to is directed atIn the case of a non-woven fabric,is a Gaussian kernel function, and has a bandwidth of hcCan be determined by cross-validation. The estimated coefficient dependent on time t is:
wherein,
and is
Estimation of function scores
To account for the main variations of the sensor signal, significant eigenvalues may be derived based on the covariance of the signal. So that KX(u, v) ═ cov (x (u), x (v)) as the covariance of the random signals collected. Coefficient [ U, V ] dependent on query time]Can be solved by the following optimization formula:
<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>min</mi> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <munder> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>z</mi> <mo>=</mo> <mn>1</mn> </mrow> </munder> <mrow> <mi>i</mi> <mo>&NotEqual;</mo> <mi>z</mi> </mrow> <msub> <mi>n</mi> <mi>j</mi> </msub> </munderover> <mi>W</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>-</mo> <mi>u</mi> </mrow> <msub> <mi>h</mi> <mi>u</mi> </msub> </mfrac> <mo>,</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mi>zj</mi> </msub> <mo>-</mo> <mi>v</mi> </mrow> <msub> <mi>h</mi> <mi>v</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> <msup> <mrow> <mo>[</mo> <msub> <mover> <mi>K</mi> <mo>^</mo> </mover> <msub> <mi>X</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>,</mo> <msub> <mi>t</mi> <mi>zj</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>B</mi> <mn>11</mn> </msub> <mi>u</mi> <mo>+</mo> <msub> <mi>B</mi> <mn>12</mn> </msub> <mi>v</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein h isuAnd hvAre respective bandwidths, ofIs the raw covariance estimated by:
K ^ X j ( t ij , t zj ) = ( X j ( t ij ) - M ^ X ( t ij ) ) ( X j ( t zj ) - M ^ X ( t zj ) ) - - - ( 11 )
due to KX(u,v)=CR(u,v)+σ2I(u=v)In which I(u=v)1 when u is V; otherwise, it is 0 }. In the case of denser signal data, each eigenvalue λsThe estimation can be done by performing numerical integration:
<math> <mrow> <msub> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>T</mi> </msubsup> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>C</mi> <mo>^</mo> </mover> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> <mi>dudv</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> </math>
the FPCA score for each unit j can be calculated by:
<math> <mrow> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>js</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>n</mi> <mi>j</mi> </msub> </munderover> <mo>[</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>M</mi> <mo>^</mo> </mover> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>ij</mi> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>
the FPCA score estimated by equation (13) approaches the sparse signal reading contaminated by the measured error. An effective alternative method to correct this problem is known as conditional expectation-Primary Analysis (PACE). Given n collected so farjAn observation itemX j=[Xj(t1j),...,Xj(tnjj)]TIn the case of (1), willThe s-th FPCA score as unit j.The conditions of (a) are desirably:
<math> <mrow> <msubsup> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>js</mi> <mo>*</mo> </msubsup> <mo>=</mo> <mi>E</mi> <mo>[</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>js</mi> </msub> <mo>|</mo> <msub> <munder> <mi>X</mi> <mo>&OverBar;</mo> </munder> <mi>j</mi> </msub> <mo>]</mo> <mo>=</mo> <msub> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <mi>S</mi> </msub> <msubsup> <munderover> <mi>&xi;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>js</mi> <mi>T</mi> </msubsup> <msubsup> <mover> <mi>&Sigma;</mi> <mo>^</mo> </mover> <mi>j</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <munder> <mi>X</mi> <mo>&OverBar;</mo> </munder> <mi>j</mi> </msub> <mo>-</mo> <msub> <munderover> <mi>M</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>X</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein at all collected measurement instants njScoring a functionPeace and quietSliding function <math> <mrow> <msub> <munderover> <mi>M</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>X</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mover> <mi>M</mi> <mo>^</mo> </mover> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>M</mi> <mo>^</mo> </mover> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <msub> <mi>n</mi> <mi>j</mi> </msub> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math> And (6) estimating.Is thatN estimated under all items ofj×njA covariance matrix. FPCA ScoringThe covariance matrix of (a) can be expressed as:
wherein,
given the estimates of all model parameters, at time tkj(k>i) Sensor signal X ofj(tkj) This can be predicted by the following equation:
<math> <mrow> <mi>E</mi> <mo>[</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <msub> <mover> <mi>M</mi> <mo>^</mo> </mover> <mi>X</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>X</mi> </msub> </munderover> <msubsup> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>js</mi> <mo>*</mo> </msubsup> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>
furthermore, it has been demonstratedThe asymptotic point-by-point standard deviation (STD) of (a) is:
<math> <mrow> <mi>STD</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <msup> <munderover> <mi>&xi;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <msub> <mover> <mi>&Omega;</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <munderover> <mi>&xi;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mover> <mi>&sigma;</mi> <mo>^</mo> </mover> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein, <math> <mrow> <munderover> <mi>&xi;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>&xi;</mi> <mo>^</mo> </mover> <msub> <mi>N</mi> <mi>X</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> </mrow> </math>
and is <math> <mrow> <msub> <mover> <mi>&Omega;</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mo>=</mo> <mi>diag</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <msub> <mi>N</mi> <mi>X</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <munderover> <mi>&theta;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>j</mi> </msub> <mo>|</mo> <msub> <munder> <mi>X</mi> <mo>&OverBar;</mo> </munder> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>
Known as Xj(tkj) The confidence interval at the desired significance level a is:
<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mo>[</mo> <mi>E</mi> <mo>[</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&alpha;</mi> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mi>STD</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>E</mi> <mo>[</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&alpha;</mi> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mi>STD</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>kj</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein z is1-α/2Is the 1-alpha/2 percentile of the standard normal distribution.
The FPCA model has been validated. In one example, a degradation condition of the same type of turbofan engine due to wear is simulated based on usage patterns (i.e., four different combinations of operating conditions and failure modes). Since different engines often operate under different operating conditions, the turbine engines are damaged to different degrees from each other. Fifteen engines were selected that were in the same combination of operating conditions (i.e., sea level) and failure mode (i.e., HPC degradation). For each engine, sensor readings are collected from 26 sensor channels, and a sensor for measuring the collected Low Pressure Turbine (LPT) outlet temperature is employed to indicate the degradation process. The training data set includes LPT readings for the period of ten engines from their start of operation to their failure. The data from the other five engines were then used as test data sets.
Note that the same verification may be employed for components of the downhole drilling tool (e.g., the drill bit). For example, sensor signals associated with multiple drill bits in their respective operations may be used as a training data set to construct an FPCA model. By using the sensor signals as a test data set, the model thus constructed can predict the performance index of the drill bit in operation. As more and more sensor signals are available, the test data set can be used accordingly to update the training data set so that the model estimation becomes more accurate.
As shown in fig. 1, different proportions of the available measurements were taken in the test data set, i.e., 50%, 60%, 70%, and 80% of the entire data set from start of run to failure of the component. From each available proportion of the signal channels, an estimate is made for the lifetime consumption or remaining useful life. The time at which the decay trend reached the preset failure threshold (1430 units of temperature in this example) was recorded as the predicted failure time. The estimated life consumption from the analysis time is calculated to provide an estimated time to failure.
In applying the FPCA model to predict the failure time, the conventional method is to use the time information as a prediction value and the amplitude information as a response variable. That is, given a known response value (i.e., a fixed magnitude threshold), the predicted value (i.e., time) will be derived from the model in reverse. Alternatively, the magnitude may be used as a predictor, while the time information is used as a response variable. Such a transformation axis facilitates mathematical calculations, since it facilitates fitting the model given a fixed oscillation value threshold as a predicted value.
The FPCA model includes an overall mean function, a number of eigenfunctions, and a function score. In this example, the bandwidth selected for the mean function is 5.9474, while the bandwidth values for the covariance function are (1.4795 ). From the training data set, the first three eigenvalues are:andabout 98.33% of the function-interpreted change (FVE).
Assuming about 95% of FVE, the FPCA model for the LPT signal based on the transformation axis can be expressed as:
<math> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>&ap;</mo> <msub> <mi>M</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </munderover> <msub> <mi>&theta;</mi> <mi>js</mi> </msub> <msub> <mi>&xi;</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&epsiv;</mi> <mi>ij</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> </math>
an FPCA model obtained from the training data set is used to predict the time to failure for each test unit given a different attainable proportion of LPT signal readings, which is used to obtain a unit specific FPCA score as solved by equation (14). In the second phase, the time to failure at the fixed LPT temperature magnitude threshold is predicted with a confidence interval of 100(1- α)% using equations (16) and (18). The reliability indicator applied here is called the Lifetime Consumption (LC):
where T (query) represents the current query time and T (failure) refers to the actual or predicted time to failure.
Another similar indicator is the remaining service life, namely:
residual service life ═ T (failure) -T (query) (21)
Therefore, the Estimated error of Estimated _ LC (Estimated lifetime consumption) compared to the actual lifetime consumption (True _ LC) at the query time is calculated using the following equation:
the predicted life consumption errors are listed in table 1 to demonstrate the performance of the FPCA model. Table 1 shows the estimation error using different data volumes (i.e., 50%, 60%, 70%, and 80% of the total signal readings over the life cycle of the monitored component). In other words, 50% means that data from the start of the tool to half its life is used in the model. As the table shows, the estimation error becomes smaller when the estimation is based on a larger set of data sets. When 80% of the data is used, the estimation error is less than 5%. Also shown in fig. 3 is the confidence interval for the LC estimate when 80% of the signal readings were collected.
Table 1: life consumption estimation performance
The model disclosed herein performs better than other models, such as a path classification and estimation model (PCE) of FPCA that combines linear regression and kernel weighted averaging. Table 2 summarizes the percentage of estimation error for the FPCA model and the PCE model. As shown, the FPCA model provides higher estimation accuracy for five test parts where signal ratios from 50% to 80% are available.
Table 2: comparison of life consumption estimation errors
Thus, as shown in FIG. 4, the method of the present disclosure includes the steps of collecting a first set of sensor signals (e.g., a training data set) and constructing a model using Functional Principal Component Analysis (FPCA) based on the first set of sensor signals, wherein the model is used to estimate one or more performance indicators of a component of a downhole drilling tool. The method also includes the steps of collecting a second set of sensor signals (e.g., a test data set) and modifying the model based on the second set of sensor signals. One or more performance indicators (e.g., probability of failure, life consumption, etc.) of the component are estimated using the modified FPCA model.
There are many variations of the systems and methods provided by the present disclosure. For example, sensor signals from different components of the drilling tool may be weighted and then combined to predict the overall life consumption of the drilling tool. The method is used to optimize drilling and exploration performance, avoid non-productive time (NPT) at the drilling site and reduce maintenance and upkeep costs.
Embodiments of the present disclosure have been described in detail. Failure embodiments will be apparent to those skilled in the art by reference to and practicing the present disclosure. Accordingly, it is intended that the specification and figures be considered as exemplary only, with a true scope of the disclosure being indicated by the following claims.

Claims (17)

1. A method for monitoring a drilling system, comprising:
collecting a first set of sensor signals;
constructing a model using Functional Principal Component Analysis (FPCA) based on the first set of sensor signals, wherein the model is used to estimate one or more performance indicators of a component of a downhole drilling tool;
collecting a second set of sensor signals;
modifying the model based on the second set of sensor signals; and
estimating one or more performance indicators of a component of the downhole drilling tool using the modified model,
wherein the sensor signal reflects one or more states of a component in the downhole drilling tool.
2. The method of claim 1, wherein the component in the drilling system is selected from the group consisting of a drill bit, a drill string, a downhole motor, an MWD/LWD instrument, a drill pipe, a drill collar, a battery, a sensor, or an alternator, a bearing, and a pump.
3. The method of claim 2, wherein the state of a component in the drilling system is selected from temperature, pressure, vibration, weight-on-bit, noise level, or RPM.
4. The method of claim 1, wherein the component in the drilling system is a Printed Circuit Board Assembly (PCBA).
5. The method of claim 1, wherein the performance indicator is selected from a probability of failure, a lifetime consumption, or a remaining useful life.
6. The method of claim 1, wherein the model comprises a plurality of model parameters, the model parameters comprising an overall mean function, a plurality of eigenfunctions, and a plurality of FPCA function scores.
7. The method of claim 1, wherein the first set of sensor signals is used as a training data set to build the model.
8. The method of claim 1, wherein the second set of sensor signals comprises a test data set.
9. The method of claim 7, wherein the first set of sensor signals comprises signal readings from the beginning of a run of a component of the downhole drilling tool to a failure of the assembly.
10. The method of claim 8, wherein the first set of sensor signals comprises signal readings from more than one operation of the same component.
11. A system for monitoring a downhole drilling tool, comprising:
a drilling assembly;
a plurality of sensors disposed with respect to the drilling assembly, wherein the sensors provide sensor signals associated with the drilling assembly;
a processor;
a non-transitory computer readable medium communicatively coupled to the processor;
a set of processor-executable instructions embodied in the non-transitory computer-readable medium, the instructions configured to implement a method comprising:
collecting a first set of sensor signals;
constructing a model using Functional Principal Component Analysis (FPCA) based on the first set of sensor signals, wherein the model is used to estimate performance indicators of components in a downhole drilling assembly;
collecting a second set of sensor signals;
modifying the model based on the second set of sensor signals; and
estimating a performance metric of a component in the downhole drilling assembly using the modified model,
wherein the sensor signal reflects at least one state of a component in the downhole drilling assembly.
12. The system for monitoring a downhole drilling tool of claim 11, wherein the drilling assembly comprises a drill bit, a drill collar, and a MWD/LWD instrument.
13. A drilling system, comprising:
a downhole drilling tool;
a plurality of sensors disposed with respect to the drilling assembly, wherein the plurality of sensors are traversed through a subterranean formation by the downhole drilling tool and generate sensor signals reflecting a state of one or more components in the downhole drilling tool;
a computer for implementing a method comprising:
collecting a first set of sensor signals;
constructing a model using Functional Principal Component Analysis (FPCA) based on the first set of sensor signals, wherein the model is used to estimate a performance indicator of a component in a downhole drilling tool;
collecting a second set of sensor signals;
modifying the model based on the second set of sensor signals; and
estimating a performance indicator of a component in the downhole drilling tool using the corrected model.
14. A drilling system according to claim 13, wherein the component of the downhole drilling tool is selected from a drill bit, a drill string, a downhole motor, a MWD/LWD instrument, a drill pipe, a drill collar, a battery, a sensor or an alternator.
15. A drilling system according to claim 14 wherein the condition of a component of the downhole drilling tool is selected from temperature, pressure, vibration, weight on bit, WOB, or RPM.
16. A drilling system according to claim 13 wherein the component of the downhole drilling tool is a printed circuit board assembly, PCBA.
17. A drilling system according to claim 13 wherein the performance indicator is selected from the group consisting of probability of failure, life consumption or remaining useful life.
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